A three-dimensional, discrete-continuum model of blood flow in microvascular networks

We introduce a hybrid, discrete-continuum method to model blood pressure across large microvascular networks with incomplete architectural information. Our multiscale approach couples a 1D Poiseuille flow description in large, discrete arteriolar and venular networks, via point sources of flux, to a continuum-based Darcy model for transport in the capillary bed. We test our hybrid framework using a vascular network imaged from the mouse brain medulla / pons using multi-fluorescence high-resolution episcopic microscopy. The fully-resolved vascular network is used to predicted the hydraulic conductivity of the capillary network and to generate a fully-discrete pressure solution to benchmark our novel method against. We show that the discrete-continuum methodology is a computationally tractable and effective tool for predicting blood pressure in real-world microvascular tissues when capillary microvessels are not well-defined. ### Competing Interest Statement The authors have declared no competing interest.